Question

Division of two irrational numbers

• A. is always a rational number
• B. is always an irrational number
• C. can be a rational number or an irrational number

Answer 1

The correct option is C can be a rational number or an irrational number

Division of two irrational numbers can be a rational number or an irrational number

Example: $\frac{\sqrt{2}}{\sqrt{8}}=\frac{\sqrt{2}}{2\sqrt{2}}=\frac{1}{2}$
Here $\frac{1}{2}$ is a rational number.

Example: $\frac{\sqrt{2}}{\sqrt{3}}=\sqrt{\frac{2}{3}}$
Here $\sqrt{\frac{2}{3}}$ is the square root of non-perfect square hence it is an irrational number.